Question

Find the equation of a line that cuts off equal intercepts on the coordinate axes and passes through the point (2, 3).

Answer 1

The equation of a line in the intercept form is
$\frac xa+\frac yb=1$ .....(i)
Here, a and b are the intercepts on x and y axes respectively.
It is given that the line cuts off equal intercepts on both the axes. This means that a = b.
Accordingly, equation (i) reduces to
$\frac xa+\frac yb=1$
⇒ $x+y=a$ .......(ii)
Since the given line passes through point (2, 3), equation (ii) reduces to
2 + 3 = a ⇒ a = 5
On substituting the value of an in equation (ii), we obtain
x + y = 5, which is the required equation of the line